Properties of Equality Worksheet
Explore and apply the properties of equality (addition, subtraction, multiplication, division, substitution, and reflexive) to solve algebraic equations.
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Standards
Topics
Properties of Equality
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Read each question carefully and apply the correct property of equality to solve or identify the property being used. Show all your work.
Complete each statement by filling in the blank with the correct property of equality.
1. If a = b, then a + c = b + c. This is the Property of Equality.
2. If x - 5 = 10, then x = 15. This is an example of the Property of Equality.
3. If 3y = 12, then y = 4. This is an example of the Property of Equality.
4. If m = n, and n = p, then m = p. This is the Property of Equality.
5. Which property justifies the step from 2x + 7 = 15 to 2x = 8?
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
6. If a = 5 and b = a + 3, then b = 5 + 3. Which property is applied here?
Reflexive Property
Symmetric Property
Transitive Property
Substitution Property
Solve each equation. Justify each step with a property of equality.
7. Solve for x: x + 9 = 20
8. Solve for y: 4y - 3 = 17
9. Solve for z: z / 5 + 2 = 6
10. A scale is balanced with 3 identical weights and a 5 kg block on one side, and a 20 kg block on the other side. Let 'w' represent the mass of one identical weight. Write an equation to represent this situation and solve for 'w', justifying each step.
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